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Estimating the structural dimension of regressions via parametric inverse regression
Author(s) -
Bura Efstathia,
Cook R. Dennis
Publication year - 2001
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/1467-9868.00292
Subject(s) - sliced inverse regression , mathematics , dimension (graph theory) , parametric statistics , inverse , bayesian multivariate linear regression , regression analysis , sufficient dimension reduction , linear regression , regression , statistics , nonparametric regression , multivariate statistics , subspace topology , parametric model , combinatorics , mathematical analysis , geometry
A new estimation method for the dimension of a regression at the outset of an analysis is proposed. A linear subspace spanned by projections of the regressor vector X , which contains part or all of the modelling information for the regression of a vector Y on X , and its dimension are estimated via the means of parametric inverse regression. Smooth parametric curves are fitted to the p inverse regressions via a multivariate linear model. No restrictions are placed on the distribution of the regressors. The estimate of the dimension of the regression is based on optimal estimation procedures. A simulation study shows the method to be more powerful than sliced inverse regression in some situations.